2025 MAST30026 Metric and Hilbert Spaces

This is still under construction.

Many administrative details about the organisation of the subject can (as always) be found in the subject handbook entry.

Consultation hours

  • TBA in Peter Hall room 166

Lecture notes

Here is the latest version of the lecture notes (updated: ).

Exercises

Here is the latest version of the exercise booklet (updated: ).

Tutorials

Tutorial classes start in week 2 of the semester. The tutorial sheets appear here at the start of the corresponding week, and solutions appear at the end of the week.

Assignments

The three assignments are posted both here and on the subject's Canvas page. Your solutions should be submitted via Canvas and Gradescope.

Assignment 1

Here is the pdf file for the first assignment, due 15 August at 20:00. If you want to write your solutions in LaTeX, here is a macros file and the template file for the first assignment.

Ed Discussion post with instructions/FAQ/errata for the first assignment.

Solutions for the first assignment.

Assignment 2

Here is the pdf file for the second assignment, due 12 September at 20:00. If you want to write your solutions in LaTeX, here is a macros file and the template file for the second assignment.

Ed Discussion post with instructions/FAQ/errata for the second assignment.

Solutions for the second assignment.

Assignment 3

Here is the pdf file for the third assignment, due 17 October at 20:00. If you want to write your solutions in LaTeX, here is a macros file and the template file for the third assignment.

Ed Discussion post with instructions/FAQ/errata for the third assignment.

Solutions for the third assignment.

Special consideration

I suggest that you familiarise yourself with the University's special consideration procedures, which have been recently overhauled.

The relevant mechanism for this subject's assignments is a short extension, which must be requested before the assignment deadline. Short means ⩽ 5 business days. You can see the rules and apply online for a short extension. (Make sure to find the form relevant to the Faculty of Science.)

If your situation is not eligible for a short extension (e.g. if the assignment deadline has passed, or an extension of 5 days would be insufficient), you may apply for special consideration. If your application is successful, this would result in waiving the assignment in question (so that the rest of the assignments are re-weighted to make up the total of 20%).

Ed discussion board

Please see the subject's Canvas page for access to the discussion board.

Lecture recordings

Please see the subject's Canvas page for access to the lecture recordings.

Other references: prerequisite knowledge

The main prerequisites for the subject are the University of Melbourne's MAST20022 Group Theory and Linear Algebra and MAST20026 Real Analysis (or some equivalent subject, see the handbook entry for details).

For those of you arriving with a different background, this means a solid understanding of linear algebra and previous exposure to abstract algebra concepts like groups, group actions, fields; also required is a firm grasp of analysis of functions on the real line.

There are many excellent abstract algebra and real analysis texts out there, so feel free to grab some to use as a reference while working on this subject.

Here are some suggestions:

Other references: metric and Hilbert spaces

There are also many excellent analysis texts out there covering various of the topics we are studying. I'll list here any that I refer to.

Note: Many of these references may be accessible via the library system either as electronic resources or physical tomes.